(7) d'y dxª -2k² d²y dx² + ky=0 k is a non-zero constant. (This equation arises in bending of elastic plate problems) HINT: substitute y = Aerx to find roots of characteristic equations r₁= r2-k; and r3= r4=-k. Roots are repeated. ANSWER: y = Aekx+Bxekx+Ce-kx+Dxe-kx

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Differential Equations

Please, show all the work and every step

(7)
d'y
dxª
-2k² d²y
dx²
+ ky=0 k is a non-zero constant.
(This equation arises in bending of elastic plate problems)
HINT: substitute y = Aerx to find roots of characteristic equations r₁= r2-k; and
r3= r4=-k. Roots are repeated.
ANSWER: y = Aekx+Bxekx+Ce-kx+Dxe-kx
Transcribed Image Text:(7) d'y dxª -2k² d²y dx² + ky=0 k is a non-zero constant. (This equation arises in bending of elastic plate problems) HINT: substitute y = Aerx to find roots of characteristic equations r₁= r2-k; and r3= r4=-k. Roots are repeated. ANSWER: y = Aekx+Bxekx+Ce-kx+Dxe-kx
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